Question

3 typists P, Q and R type some pages. The first two typists P and Q
who are typing constantly, can do a work as long as the third typist R
does alone. If the same work can be done by the second typist alone,
in less than 5 hours before the first typist and in 4 hours more in
comparison with the third typist, how long will Q and R take to com-
plete this work together ?​

Answer 1

Answer:

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Answer 2

Answer:

3.75 hr

Step-by-step explanation:

Consider Total work = 1

Total work = One day work * no. of days

Let consider Time taken by R be x.

Q takes 4 hr more than R, Q = x + 4

P takes 5 hr more than Q, and thus 9 hr more than R, P = (x + 4) + 5 = x + 9

$one \: day \: work \: by \: R \: in \: x \: hrs = \frac{1}{x} \\ one \: day \: work \: by \: p \: in \: (x + 9) \: hrs = \frac{1}{x + 9} \\ one \: day \: work \: by \: q \: in \: (x + 4)\: hrs = \frac{1}{x + 4}$

Given that P and Q together do the same amount of work as done R in same period of time.

Hence

$\frac{1}{x + 9} + \frac{1}{x + 4} = \frac{1}{x} \\ \frac{2x + 13}{ {x}^{2} + 13x + 36} = \frac{1}{x}$

$2 {x}^{2} + 13x = {x}^{2} + 13x + 36$

${x}^{2} = 36$

$x = 6$

time taken by R = 6 hr

time taken by Q = x + 4 = 10 hr

One day work of Q and R working together be 1/10 + 1/6

$\frac{1}{10} + \frac{1}{6} = \frac{8}{30}$

Time taken by Q and R to complete whole work = total work / one day work

$time \: taken \: = \frac{30}{8} = 3.75 \: hr$